主动配电网三相电压优化模型的线性化技术探讨

The linearization technology of the active power distribution network for optimized model of three-phase voltage

三相主动配电网的优化调度实质上是一个求解非凸的混合整数二阶锥非线性规划问题,缺乏严格高效的求解方法。本文采用二阶锥松弛技术将其中的三相潮流方程进行了凸化松弛,将一个非凸非线性规划问题转化为由一系列线性不等式和线性等式组成的线性规划模型。以扩展的标准IEEE 33节点三相测试系统构建算例,采用青海省某地区一天12个时刻的负荷数据和光伏预测数据进行了验证。静态优化的结果表明:二阶锥形式的潮流方程利用线性多项式拟合之后得到的电压值和原始二阶锥的结果高度一致,验证了这一线性化方法的可行性;动态优化的结果显示:线性规划模型中引入储能装置、分布式电源、静止无功补偿装置、分组投切电容器组的优化调度策略,电压变化率在2%之内,最大网络损耗仅有0.07 MW,最大松弛误差在6×10^(-6)之内,表明基于上述线性规划模型的主动配电网动态优化的可行性、精确性和有效性。

The optimal scheduling of three phase active power distribution network is essentially a non-convex mixed integer two order nonlinear programming problem. In this paper,the three-phase power flow equation was convex relaxed with two order cone relaxation technique. A non-convex nonlinear programming problem was transformed into a linear programming model that composes of a series of linear inequalities and linear equation. An example of the extended standard IEEE33 node test system was built,and verified by the load data of 12 days in a certain area of Jiangsu Province and the photovoltaic forecast data. Static optimization results show that by introducing optimized scheduling strategy,such as,energy storage device,distributed power supply,static reactive compensation device,packet switched capacitor group into linear programming model,the change rate of the voltage is strictly controlled within 2% and the biggest loss is only 0. 07 MW. The maximum error is smaller than 6 × 10^(-6). These suggest the feasibility,effectiveness and accuracy of active distribution network dynamic optimization of the linear programming model.